In this paper, we show that a one-dimensional (1D) asymptotic theory, formulated as coupled nonlinear ordinary differential equations (ODEs), can capture the impact of surfactant at low concentrations in long 3D channels bounded by periodic SHSs, where diffusion is strong enough to suppress cross-channel concentration gradients.
We overcome a shortcoming of pre-existing theories by using systematic analysis and by avoiding assumptions deployed in prior scaling arguments.
This allows us to address non-uniform shear stresses at the liquid–gas interface, providing a model of advection-dominated regimes for surfactant-contaminated SHSs.
By mapping the drag reduction across a large part of the high-dimensional parameter space, we identify a multitude of asymptotic regions and their boundaries, yet unexplored by previous theories [1]}, [2]}, [3]}.
Closed-form asymptotic solutions predict the drag reduction in all the regions of the parameter space studied, offering analytical predictions for practical use where numerical simulation of the fluid and surfactant equations are computationally expensive [2]}.
By addressing the role of shear dispersion, the theory developed here constitutes also a stepping stone towards a wider class of laminar flows with weaker diffusion, where the bulk concentration field varies in 3D and must be resolved numerically.
